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Geometry of Grassmannian Lagrangian manifolds and their submanifolds, with applications to nonlinear partial differential equations of physical interest

Total Cost €


EC-Contrib. €






 GEOGRAL project word cloud

Explore the words cloud of the GEOGRAL project. It provides you a very rough idea of what is the project "GEOGRAL" about.

ferapontov    sophisticated    bridge    theory    designed    dimensional    he    clarified    contact    corresponding    strengthen    integrable    direction    gave    examples    geometry    continuity    consists    moving    initiated    cartan    boundary    variational    theories    manno    classify    monge    submanifolds    normal    economy    re    scientific    amp    nonlinear    varieties    characterise    fbv    equations    planes    isotropic    attempts    hyd    contribution    hydrodynamic    bundles    frame    topological    disciplines    bisecant    rare    spaces    turn    integral    himself    grassmannians    theoretical    prolongation    profile    manifold    cast    lines    space    3rd    parallelism    rational    alekseevsky    invariant    cauchy    flags    maximal    1st    sciences    discovered    applicative    mov    egrave    hma    regard    structures    continue    evident    bonds    geogral    natural    homogeneous    scope    structure    free    lagrangian    relevance    tested    pdes    jet    symplectic    curve    meta    geometric    certain   

Project "GEOGRAL" data sheet

The following table provides information about the project.


Organization address
address: UL. SNIADECKICH 8
postcode: 00 956

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Poland [PL]
 Project website
 Total cost 146˙462 €
 EC max contribution 146˙462 € (100%)
 Programme 1. H2020-EU.1.3.2. (Nurturing excellence by means of cross-border and cross-sector mobility)
 Code Call H2020-MSCA-IF-2014
 Funding Scheme MSCA-IF-EF-ST
 Starting year 2015
 Duration (year-month-day) from 2015-09-01   to  2017-08-31


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 


 Project objective

The aim of GEOGRAL is to strengthen the bonds of the geometric theory of nonlinear PDEs (and, in particular, integrable systems and equations of Monge-Ampère type) with the geometry of Lagrangian Grassmannians and their submanifolds. In spite of the evident parallelism between these two disciplines, attempts have been rare, yet sophisticated, to cast a bridge between them, and the Applicant himself already gave his own contribution in this direction: he clarified the structure of the space of non-maximal integral elements of the contact planes in jet spaces and studied 3rd order Monge-Ampère equations (which turn out to be of key relevance in topological field theories) through the so-called meta-symplectic structure on the 1st prolongation of a contact manifold. GEOGRAL has a wide applicative scope, as its theoretical results can be tested on equations and variational problems of key importance for Natural Sciences, Technology and Economy. Tailored to the Applicant's scientific profile and designed in continuity with his previous and current research activities, GEOGRAL consists of four research lines: [MOV] Regard Lagrangian Grassmannians as homogeneous spaces and and use Cartan's method of moving frame to classify their submanifolds, as in D. The's work, and characterise the corresponding invariant equations, in continuity with D. Alekseevsky's work. [HYD] Continue the study of certain rational normal curve bundles on Lagrangian Grassmannians, and their bisecant varieties, which are associated with integrable systems of hydrodynamic type, discovered by E. Ferapontov. [HMA] Geometric study of multi-dimensional and higher-order Monge-Ampère equations, initiated by G. Manno and the Applicant. [FBV] Study some examples of Cauchy problems and variational problems with free boundary values by exploiting the geometric structures on the spaces of isotropic flags and non-maximal isotropic elements of a meta-symplectic space, in continuity with the Applicant's own work.


year authors and title journal last update
List of publications.
2017 A. J. Bruce, K. Grabowska, G. Moreno
On a Geometric Framework for Lagrangian Supermechanics
published pages: , ISSN: 1941-4889, DOI:
Journal of Geometric Mechanics 2019-07-23
2016 Giovanni Moreno, Monika Ewa Stypa
Geometry of the free-sliding Bernoulli beam
published pages: , ISSN: 1804-1388, DOI: 10.1515/cm-2016-0011
communications in mathematics 2 issues/vol./yr. 2019-07-23
2017 Giovanni Moreno
An introduction to completely exceptional 2nd order scalar PDEs
published pages: , ISSN: , DOI:
2016 Gianni Manno, Giovanni Moreno
Meta-Symplectic Geometry of 3 rd Order Monge-Ampère Equations and their Characteristics
published pages: , ISSN: 1815-0659, DOI: 10.3842/SIGMA.2016.032
Symmetry, Integrability and Geometry: Methods and Applications 2019-07-23
2016 Jan Gutt, Gianni Manno, Giovanni Moreno
Completely exceptional 2nd order PDEs via conformal geometry and BGG resolution
published pages: , ISSN: 0393-0440, DOI: 10.1016/j.geomphys.2016.04.021
Journal of Geometry and Physics 2019-07-23

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